# Binary search algorithms

## Functions
template<typename ForwardIterator, typename Type> ForwardIterator | std::lower_bound (ForwardIterator first, ForwardIterator last, const Type &__val)
| Finds the first position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type, typename Compare> ForwardIterator | std::lower_bound (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
| Finds the first position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type> ForwardIterator | std::upper_bound (ForwardIterator first, ForwardIterator last, const Type &__val)
| Finds the last position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type, typename Compare> ForwardIterator | std::upper_bound (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
| Finds the last position in which val could be inserted without changing the ordering.
template<typename ForwardIterator, typename Type> pair< ForwardIterator, ForwardIterator > | std::equal_range (ForwardIterator first, ForwardIterator last, const Type &__val)
| Finds the largest subrange in which val could be inserted at any place in it without changing the ordering.
template<typename ForwardIterator, typename Type, typename Compare> pair< ForwardIterator, ForwardIterator > | std::equal_range (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
| Finds the largest subrange in which val could be inserted at any place in it without changing the ordering.
template<typename ForwardIterator, typename Type> bool | std::binary_search (ForwardIterator first, ForwardIterator last, const Type &__val)
| Determines whether an element exists in a range.
template<typename ForwardIterator, typename Type, typename Compare> bool | std::binary_search (ForwardIterator first, ForwardIterator last, const Type &__val, Compare comp)
| Determines whether an element exists in a range.

## Detailed Description

These algorithms are variations of a classic binary search. They all assume that the sequence being searched is already sorted.

The number of comparisons will be logarithmic (and as few as possible). The number of steps through the sequence will be logarithmic for random-access iterators (e.g., pointers), and linear otherwise.

The LWG has passed Defect Report 270, which notes: The proposed resolution reinterprets binary search. Instead of thinking about searching for a value in a sorted range, we view that as an important special case of a more general algorithm: searching for the partition point in a partitioned range. We also add a guarantee that the old wording did not: we ensure that the upper bound is no earlier than the lower bound, that the pair returned by equal_range is a valid range, and that the first part of that pair is the lower bound.

The actual effect of the first sentence is that a comparison functor passed by the user doesn't necessarily need to induce a strict weak ordering relation. Rather, it partitions the range.

## Function Documentation

template<typename ForwardIterator, typename Type, typename Compare>
bool binary_search | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val,
|  | Compare | comp
| ) |

  | Determines whether an element exists in a range. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
  | comp | A functor to use for comparisons.
Returns: True if val (or its equivelent) is in [first,last ]. Note that this does not actually return an iterator to val. For that, use std::find or a container's specialized find member functions. The comparison function should have the same effects on ordering as the function used for the initial sort. Definition at line 3941 of file stl_algo.h. References std::lower_bound().

template<typename ForwardIterator, typename Type>
bool binary_search | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val
| ) |

  | Determines whether an element exists in a range. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
Returns: True if val (or its equivelent) is in [first,last ]. Note that this does not actually return an iterator to val. For that, use std::find or a container's specialized find member functions. Definition at line 3909 of file stl_algo.h. References std::lower_bound().

template<typename ForwardIterator, typename Type, typename Compare>
pair<ForwardIterator, ForwardIterator> equal_range | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val,
|  | Compare | comp
| ) |

  | Finds the largest subrange in which val could be inserted at any place in it without changing the ordering. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
  | comp | A functor to use for comparisons.
Returns: An pair of iterators defining the subrange. This is equivalent to
        std::make_pair(lower_bound(first, last, val, comp),
                       upper_bound(first, last, val, comp))
but does not actually call those functions. Definition at line 3851 of file stl_algo.h. References std::advance(), std::distance(), std::lower_bound(), and std::upper_bound().

template<typename ForwardIterator, typename Type>
pair<ForwardIterator, ForwardIterator> equal_range | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val
| ) |

  | Finds the largest subrange in which val could be inserted at any place in it without changing the ordering. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
Returns: An pair of iterators defining the subrange. This is equivalent to
        std::make_pair(lower_bound(first, last, val),
                       upper_bound(first, last, val))
but does not actually call those functions. Definition at line 3789 of file stl_algo.h. References std::advance(), std::distance(), std::lower_bound(), and std::upper_bound().

template<typename ForwardIterator, typename Type, typename Compare>
ForwardIterator lower_bound | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val,
|  | Compare | comp
| ) |

  | Finds the first position in which val could be inserted without changing the ordering. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
  | comp | A functor to use for comparisons.
Returns: An iterator pointing to the first element "not less than" val, or end() if every element is less than val. The comparison function should have the same effects on ordering as the function used for the initial sort. Definition at line 2665 of file stl_algo.h. References std::advance(), and std::distance(). Referenced by std::map< Key, Type, Compare, Allocator >::operator[]().

template<typename ForwardIterator, typename Type>
ForwardIterator lower_bound | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val
| ) |

  | Finds the first position in which val could be inserted without changing the ordering. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
Returns: An iterator pointing to the first element "not less than" val, or end() if every element is less than val. Definition at line 2610 of file stl_algo.h. References std::advance(), and std::distance(). Referenced by std::binary_search(), and std::equal_range().

template<typename ForwardIterator, typename Type, typename Compare>
ForwardIterator upper_bound | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val,
|  | Compare | comp
| ) |

  | Finds the last position in which val could be inserted without changing the ordering. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
  | comp | A functor to use for comparisons.
Returns: An iterator pointing to the first element greater than val, or end() if no elements are greater than val. The comparison function should have the same effects on ordering as the function used for the initial sort. Definition at line 2764 of file stl_algo.h. References std::advance(), and std::distance().

template<typename ForwardIterator, typename Type>
ForwardIterator upper_bound | ( | ForwardIterator | first,
|  | ForwardIterator | last,
|  | const Type & | __val
| ) |

  | Finds the last position in which val could be inserted without changing the ordering. Parameters:
  | first | An iterator.
  | last | Another iterator.
  | val | The search term.
Returns: An iterator pointing to the first element greater than val, or end() if no elements are greater than val. Definition at line 2712 of file stl_algo.h. References std::advance(), and std::distance(). Referenced by std::equal_range().